Review: The algebraic relational theory and its applications

This Review concerns the Algebraic Relational Theory of living systems as developed by Leguizamon and co-workers since 1973 and based on the categorical approach championed by Robert Rosen and his (M,R) systems. The Algebraic Relational Theory expanded, by using new mathematical developments such as lattice theory, the relational notions found in (M,R) systems with concepts such as material physical nature and extrinsic energy that reflect aspects of physical reality not captured by standard physical concepts like mass, energy or time. The Algebraic Relational Theory is another effort in the direction of developing a theory about the notion of biological organization. The Review contains the foundations of the theory, the principal mathematical developments, and applications of the theoretical results to different biological problems. They are the substantial base from which new ideas could be developed. It also includes a synthesis of initial experiments connected with this area of research. Carlos Leguizamon died in 1998. We had worked together for 20 years.